Ratio, proportion and rates of change worksheet — GCSE Foundation

1.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.

2.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

3.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

4.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?

5.A necklace uses 22 blue beads and 8 red beads. Write the number of blue beads as a fraction of the number of red beads. Give your answer as a mixed number in its simplest form.

6.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.

7.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.

8.Work out the time taken to travel 120 km at an average speed of 60 km/h.

9.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.

10.Two numbers are in the ratio 2 : 3. The smaller number is 8. Work out the larger number.

11.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.

12.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.

13.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.

14.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.

15.A plan of a garden is drawn to a scale of 1 : 200. A path measures 3 cm on the plan. Work out the real length of the path, in centimetres.